Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks (international standard IEEE 802.3). On Ethernet, any Network Interface Card (NIC) can try to send a packet in a channel at any time. If another NIC tries to send a packet at the same time, a collision is said to occur and the… (More)

We consider Lehmann-Rabin’s randomized solution to the well-known problem of the dining philosophers. Up to now, such an analysis has always required a “fairness” assumption on the scheduling mechanism: if a philosopher is continuously hungry then he must eventually be scheduled. In contrast, we modify here the algorithm in order to get rid of the fairness… (More)

Timed models were introduced to describe the behaviors of real-time systems and they were usually required to produce only executions with divergent sequences of times. However, when some physical phenomena are represented by convergent executions, Zeno words appear in a natural way. Moreover, time can progress if such an infinite execution can be followed… (More)

Statistical model-checking is an alternative verification technique applied on stochastic systems whose size is beyond numerical analysis ability. Given a model (most often a Markov chain) and a formula, it provides a confidence interval for the probability that the model satisfies the formula. One of the main limitations of the statistical approach is the… (More)

We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton’s nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be… (More)